On Two-Current Realization of KP Hierarchy

TL;DR

This paper presents a novel two-current framework for the KP hierarchy, exploring its algebraic structures, deformations, and applications to integrable models like Toda and WZNW, highlighting new connections and properties.

Contribution

It introduces a simple two-current description of the KP hierarchy and links it to W-infinity algebras, expanding understanding of nonlinear integrable systems.

Findings

Established a deformation scheme connecting W-infinity algebras

Analyzed properties of Faà di Bruno polynomials in this context

Applied the framework to Toda models, WZNW, and discrete KP

Abstract

A simple description of the KP hierarchy and its multi-hamiltonian structure is given in terms of two Bose currents. A deformation scheme connecting various W-infinity algebras and relation between two fundamental nonlinear structures are discussed. Properties of Fa\'a di Bruno polynomials are extensively explored in this construction. Applications of our method are given for the Conformal Affine Toda model, WZNW models and discrete KP approach to Toda lattice chain.